1 We don't usually
write x (times) in
an equation when
multiplying, we
instead just put
the number in
front of the
bracket. (Example:
3y(4-2y), not 3y x
(4-2y)
2 Distributive Law
2.1 a(b+c)
2.1.1 We expand it by
multiplying the
number outside the
bracket with both
numbers inside the
bracket.
2.2 (a+b)(c+d)
2.2.1 we do this by
multiplying by using
SLIP.
3 Perfect Squares
3.1 (a+b)^2
3.2 We get our answer
by expanding the
brackets, and then
simplifying it later,
3.2.1 In general:
4 Difference of 2 Squares
4.1 (a+b)(a-b)
4.1.1 Method: We will first
have to expand the
brackets, which will
be a^2 +ab -ab
-b^2. We will then
need to simplify the
terms and it will
become a^2 - b^2.
4.2 When we
simplify, the two
middle terms
cancel out.
4.2.1 Examp,e:
5 Simplifying
5.1 We simplify equations by
finding the common factors,
and then we simplify.
5.2 This is so that we
can see the
equations in a
much easier way.
5.3 Example:
6 Expanding
6.1 Expanding expression with brackets
6.1.1 When there is a negative term
outside the bracket, the sign of
the multiplied terms change.
6.1.1.1 Example:
6.1.2 To expand, we have
to multiply every
term inside a
bracket by the term
outside the bracket.
6.1.2.1 Example:
6.1.3 Expanding brackets and simplifying
6.1.3.1 Sometimes, we
need to multiply out
brackets then
simplify.
6.1.3.1.1 Multiplying out
both brackets or
terms and
collecting like
terms.
6.1.3.2 Examples:
6.2 We have to multiply
the bracket in order
to expand it.